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Conformal measures for meromorphic maps

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dc.abstract.enIn this paper we study relations between the existence of a conformal measure on the Julia set J(f) of a transcendental meromorphic map f and the existence of a zero of the topological pressure function P(f, t) for the map f (with respect to the spherical metric). In particular, we show that if f is hyperbolic and admits a t-conformal measure which is not totally supported on the set of escaping points of f, then P(f, t) = 0. On the other hand, for a wide class of maps f, including arbitrary maps with at most finitely many poles and finite set of singular values as well as hyperbolic maps with at most finitely many poles, if P(f, t) = 0, then there exists a t-conformal measure on J(f). This partially answers a question of R.D.Mauldin.
dc.affiliationUniwersytet Warszawski
dc.contributor.authorKarpińska, Bogusława
dc.contributor.authorBarański, Krzysztof
dc.contributor.authorZdunik, Anna
dc.date.accessioned2024-01-24T20:06:11Z
dc.date.available2024-01-24T20:06:11Z
dc.date.issued2018
dc.description.financeNie dotyczy
dc.description.number1
dc.description.volume43
dc.identifier.doi10.5186/AASFM.2018.4329
dc.identifier.issn1239-629X
dc.identifier.urihttps://repozytorium.uw.edu.pl//handle/item/103539
dc.identifier.weblinkhttp://www.acadsci.fi/mathematica/Vol43/vol43pp0247-0266.pdf
dc.languageeng
dc.pbn.affiliationmathemathics
dc.relation.ispartofAnnales Academiae Scientiarum Fennicae Mathematica
dc.relation.pages247-266
dc.rightsClosedAccess
dc.sciencecloudnosend
dc.subject.enmeromorphic functions, Julia sets, conformal measures, topological pressure
dc.subject.plfunkcje meromorficzne, zbiory Julii, miary konforemne, cisnienie topologiczne
dc.titleConformal measures for meromorphic maps
dc.typeJournalArticle
dspace.entity.typePublication